Chapter 17, Problem 1STP

Interpretation Introduction

Interpretation: The amount of heat required to melt a given amount of ethanol is to be calculated.

Concept introduction:

Enthalpy of fusion is defined as the heat change associated with the change in the state of matter from solid to liquid. It is represented by the symbol ${\text{ΔH}}_{\text{fus}}$ and measured in $\text{kJ/mol}$ .

Answer to Problem 1STP

  $2.63\text{ kJ}$

Explanation of Solution

  ${\text{ΔH}}_{\text{fus}}$ of ethanol is given to be $\text{4}\text{.93 kJ/mol}$

It is given that when $\text{1 mol}$ of ethanol melts at its freezing point, the energy required is $\text{4}\text{.93 kJ}$

Given the amount of ethanol = $\text{24}\text{.5 g}$

Moles of a substance is found by dividing the given amount of substance by the molecular mass of the substance.

  $\begin{array}{l}\text{moles of ethanol}=\frac{\text{given amount of ethanol}}{\text{Molar mass of ethanol}}\\ \text{moles of ethanol}=\frac{\text{24}\text{.5g}}{\text{46}\text{.07 g/mol}}=0.532\text{mol}\end{array}$

To melt $\text{1 mol}$ of ethanol, the heat required is = $\text{4}\text{.93 kJ}$

Thus, to melt $0.532\text{mol}$ of ethanol, the heat required is = $\frac{4.93\text{ kJ}}{\text{1 mol}}\times 0.532\text{ mol}=2.63\text{ kJ}$